Assignment 2
Group L01G02
Tyler Sitchon, Ethan Cunanan, Johan Kok, Tingwei Liang and Jerry Jin
Introduction
Aim: Determine if there is a model to conveniently measure body fat percent at home
Data Description
Dataset Source:
- Sourced from BYU Human Performance Research Center
- Directed by Mark Ricard
Data Wrangling: BF Percent
![]()
Reducing Outliers
Siri equation
\[
Pct.BF = \frac{495}{density} - 450
\]
Wrangling cont.
Incorrect Results
- Body density of the human body typically falls within the range of 0.900 to 1.100 g/cm³ (Jackson & Pollock, 2007)
Exploratory Data Analysis: Scatter plots
Exploratory Data Analysis: Correlation Analysis
Checking Assumptions: Multicollinearity
Checking Assumptions: Homoscedacity and Normality
Residual plots
Stepwise Regression and Stepwise Subset Selection
Model 1 - Bidirectional
Model 2 - Backwards
Model 3 - Forwards
Cross Validation
Cross Validation Results
Comparison of Stepwise Regression Models
| Bidirectional |
4.367317 |
0.7179396 |
22.91053 |
| Backward |
4.433432 |
0.7222846 |
23.25736 |
| Forward |
4.428418 |
0.7246442 |
23.23106 |
Generalized Least Squares (GLS)
Overview of GLS
- Purpose: GLS accounts for heteroscedasticity and Multicollinearity, providing more reliable estimates when these issues are present.
Bootstrapping
Overview
- Purpose: Bootstrapping is a resampling technique that generates an empirical distribution of estimated parameters by repeatedly sampling from the original dataset.
Bootstrapping
Discussion of Results
Derived Variables
- We would also like to investigate the effectiveness of using common measurements derived from the variables in our models
Body Mass Index (BMI) where:
\[
\text{BMI} = \frac{\text{Weight(lb)}}{\text{Height(inches)}} \cdot 703
\]
Waist-Hip Ratio (WHR) where:
\[
\text{WHR} = \frac{\text{Waist Circumference}}{\text{Hip Circumference}}
\]
Limitations
1. Sample Representativeness Issues
2. Potential Confounding Factors
3. Assumption of Linearity
Further Directions
1. Incorporating More Nonlinear Models
2. Increasing Sample Diversity
3. Model Ensemble Techniques